# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Dimension of the attractors associated to the Ginzburg-Landau partial differential equation. (English) Zbl 0623.58049
We study the long-time behavior of solutions to the Ginzburg-Landau partial differential equation. It is shown that a finite-dimensional attractor captures all the solutions. An upper bound on this dimension is given in terms of physical quantities, by estimating the Lyapunov exponents on the trajectories. Finally, using the well-known side-band instabilities of an exact, time-dependent solution (Stokes solution) we derive lower bounds on the dimension of the universal attractor. Moreover the lower and upper bounds agree.
##### MSC:
 58Z05 Applicatons of global analysis to physics 35Q99 PDE of mathematical physics and other areas 37C70 Attractors and repellers, topological structure